Complex Integration in MATLAB with symbolic integration limits

I'm having trouble with integrating this using MATLAB. When i try and run it as shown below, the answer that comes out i'm pretty sure is wrong. This is the first time i'm using matlab to help with integration so apologies in advance if i'm doing something very silly. Can anyone give me some pointers as to what i'm doing wrong?

syms y b n_1 n_2 R

b_y = (b-((b-(b/4))/(n_1+n_2))*y);
x = (y^2*b_y)/(1+(y/R));
I = int(x,-n_1,n_2)

I = 

[Torsten]

Any assumptions on the parameters n_1, n_2, b or R that could help simplifying the result ?

[Elliott Kitson]

Hello, So R, n_1, and n_2 will be constants i believe, and b is also a fixed value (its the max value of b(y) when y is at n_1)

[Torsten]

Any assumptions on the parameters n_1, n_2, b or R that could help simplifying the result ?

E.g. is -R in the interval of integration (thus in the interval [-eta1 eta2]) so that your function would have a pole ? Are eta1 and eta2 positive ? Are all parameters involved real numbers or can they be complex ?

[Elliott Kitson]

What do you mean by "is -R in the interval of integration"? - Really sorry, i'm not familiar with that term. But eta1 and eta2 are both positive values and all parameters involved are real numbers. Appreciate your time helping! :)

[Torsten]

What do you mean by "is -R in the interval of integration"?

If -R is in the interval [-eta1 eta2], the denominator of your integrand becomes 0 and your integrand +/- Infinity or NaN.

Similar to

syms x
f = 1/(1-x);
int(f,x,0.5,1.5)

ans = 

NaN

Answer 1

[Torsten]

Does this help ?

Note that no distiction is made about the R-value. But you should keep in mind that the answer is incorrect if -R is in the interval [-eta1 eta2].

syms y b n_1 n_2 R
b_y = (b-((b-(b/4))/(n_1+n_2))*y);
x = (y^2*b_y)/(1+(y/R));
I = int(x,y);
simplify(subs(I,y,n_2)-subs(I,y,-n_1))

ans = 

[Elliott Kitson]

From looking into it, if I’m not mistaken R only causes an issue if it is equal to or less than eta_1, which in this situation, would never be the case. R is always greater than eta_1.Does this then mean that the solution you provided below would be valid?

[Torsten]

Does this then mean that the solution you provided below would be valid?

Yes.

[Elliott Kitson]

Thanks for the help! Massively appreciate it :)